An automatic parking brake is known for example from DE 10 2012 202 962 A1. With such automatic parking brakes a clamping force is applied to a brake disk by means of a spindle drive that is driven by an electric motor. The automatic parking brakes of the type discussed here are those without a Hall sensor or other sensors for calculating the revolution rate of the motor. Rather, the clamping and release process of the automatic parking brake is essentially controlled using an analysis of the motor voltage and of the motor current, giving information about the travel of the spindle and the clamping force of the brake by the use of a suitable algorithm. Parking systems of this type have the advantage that no sensors are necessary and the braking force can be estimated within the control electronics, which enables them to be disposed spatially separately from the brake motors. The challenge with the automatic parking brakes operated without sensors is that lower accuracy must be accepted during the clamping and release process. In particular, during the release process the problem arises that the motor currents are very low because of the reducing clamping force. During the measurement of the low motor currents, measurement errors that cannot be compensated can occur because of sometimes considerable measurement deviations, which remain undetected despite redundant detection of the motor currents and voltages. The measurement errors can thus result in an incorrect calculation of the travel of the spindle nut and thus in insufficient opening of the automatic parking brake and a resulting residual drag torque.